M4502 Mathematical Analysis 4

Faculty of Science
Spring 2008 - for the purpose of the accreditation
Extent and Intensity
2/2/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Jaromír Šimša, CSc. (lecturer)
Guaranteed by
doc. RNDr. Eduard Fuchs, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Zuzana Došlá, DSc.
Prerequisites
Knowledge of the differential and integral calculus in the one variable and basic knowledge on metric spaces.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Ordinary differential equations. Infinite number series. Sequencies and series of functions. Jordan measure in the plane.
Syllabus
  • Ordinary differential equations: elementary methods of solution of first order differential equations, second order linear differential equations with constant coefficients. Infinite number series: sum of series, operations with series, convergence criteria, absolute convergence. Sequencies and series of functions: uniform convergence, integration and derivation of series, power series, Taylor series. Jordan measure in the plane.
Literature
  • Diferenciální počet. Edited by Vojtěch Jarník. Vyd. 3., dopl. Praha: Academia, 1976, 669 s. URL info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. info
  • DOŠLÁ, Zuzana, Roman PLCH and Petr SOJKA. Matematická analýza s programem Maple. Díl 2, Nekonečné řady. (The Multivariable Calculus with program Maple. Part 2, Infinite series.). prvni. Brno: Masarykova univerzita, 2002, 453 pp. Matematická analýza s programem Maple, 2. ISBN 80-210-3005-4. Domovská stránka projektu Domovská stránka Díl 1. info
  • PLCH, Roman, Zuzana DOŠLÁ and Petr SOJKA. Matematická analýza s programem Maple. Díl 1, Diferenciální počet funkcí více proměnných. (The Multivariable Calculus with program Maple. Part 1, Differencial calculus). prvni. Brno: Masarykova Universita, 1999, 80 pp. ISBN 80-210-2203-5. URL info
  • RÁB, Miloš. Metody řešení obyčejných diferenciálních rovnic. 3. vyd. Brno: Masarykova univerzita, 2004, ii, 96. ISBN 8021034165. info
Bookmarks
https://is.muni.cz/ln/tag/PříF:M4502!
Assessment methods (in Czech)
Přednáška a cvičení.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020.